Profiling the binding motif between Be and Mg in the ground state via a single-reference coupled cluster method

We present a study on the performance of our iterative triples correction for the coupled cluster singles and doubles excitations (CCSDT-1a+d) method for computation of potential energy surface (PES), spectroscopic constants, and vibrational spectrum for the ground state (X¹Σ⁺) BeMg, where the ostensible inadequacy of the CCSD and CCSD(T) methods is quite expected. We compare our results with those obtained using state-of-the-art multireference configuration interaction (MRCI) investigations reported earlier by Kerkines and Nicolaides. Our estimated dissociation energy (417.37 cm^?1), equilibrium distance (3.285 Å), and vibrational frequency (82.32 cm^?1) are in good agreement with recent results of advanced MRCI calculations for X¹Σ⁺ BeMg PES, which exhibits a shallow well of 469.4 cm^?1 with a minimum at 3.241 Å and a harmonic vibrational frequency of 85.7 cm^?1. Very weakly bound nature of X¹Σ⁺ BeMg is clearly reflected from these values. In accord with MRCI studies, a comparison of BeMg with iso-valence weakly bound ground-state species, Be₂ and Mg₂, suggests that its characteristics do not exhibit any resemblance to Be₂ rather, it shows a close kinship to Mg₂. The agreement of our derived vibrational levels with those obtained via the high-level MRCI calculations is very encouraging reflecting the potential of the suitably modified single-reference coupled cluster (SRCC) method, CCSDT-1a+d as a tool for the study of multireference van der Waals systems.     

Multireference configuration interaction potential curve and analytical potential energy function of the ground and low-lying excited states of CdSe

The potential energy curves (PECs) of the ground state ($^{3}\Pi )$ and three low-lying excited states ($^{1}\Sigma $, $^{3}\Sigma $,$^{ 1}\Pi )$ of CdSe dimer have been studied by employing quasirelativistic effective core potentials on the basis of the complete active space self-consistent field method followed by multireference configuration interaction calculation. The four PECs are fitted to analytical potential energy functions using the Murrel--Sorbie potential function. Based on the PECs, the vibrational levels of the four states are determined by solving the Schr\"{o}dinger equation of nuclear motion, and corresponding spectroscopic constants are accurately calculated. The equilibrium positions as well as the spectroscopic constants and the vibrational levels are reported. By our analysis, the $^{3}\Pi $ state, of which the dissociation asymptote is Cd($^{1}$S) + Se($^{3}$P), is identified as a ground state of CdSe dimer, and the corresponding dissociation energy is estimated to be 0.39\,eV. However, the first excited state is only 1132.49\,cm$^{ - 1}$ above the ground state and the $^{3}\Sigma $ state is the highest in the four calculated states.     

HOF分子非谐性力场、光谱常数和振动能级的迭代三激发耦合簇计算

采用包含迭代三激发的耦合簇理论（ CC3和CCSDT-3）,在aug-cc-pVTZ基组水平上对HOF分子几何构型进行优化。通过解析二阶导数结合有限差分技术获得HOF二阶、完全三阶和半对角四阶力场。通过非谐性分析,得到其基频、旋振相互作用常数、非谐性常数和离心畸变光谱常数。应用二阶振动微扰理论（VPT2）得到HOF多个泛频峰位置。目前计算值与实验及其它文献结果符合良好。     

HOF分子非谐性力场、光谱常数和振动能级的迭代三激发耦合簇计算

采用包含迭代三激发的耦合簇理论(CC3和CCSDT-3), 在aug-cc-pVTZ基组水平上对HOF分子几何构型进行优化. 通过解析二阶导数结合有限差分技术获得HOF二阶、完全三阶和半对角四阶力场. 通过非谐性分析, 得到其基频、旋振相互作用常数、非谐性常数和离心畸变光谱常数. 应用二阶振动微扰理论(VPT2)得到HOF多个泛频峰位置. 目前计算值与实验及其它文献结果符合良好.     

SiH自由基分子激发态的多参考组态相互作用计算简

运用含Davidson修正的多参考组态相互作用(MRCI+Q)方法,在def2-qzvpp基组水平上对SiH自由基分子对应最低三个离解限Si(3 P,1 D,1 S)+H(2 S)的共6个双重态X2Π,A2Δ,B2∑-,C2∑+,D2∑+,F2Π和2个四重态a4∑-,b4 P在0.1nm~0.6nm范围内进行了势能扫描计算.得出X2Π,A2Δ和a4∑-态为典型的束缚态,其离解能分别为3.17eV,0.96eV和1.49eV,平衡核间距分别为0.1523nm,0.1533nm和0.1499nm.其中B2∑-态在接近基态平衡核间距处与A2Δ态极为靠近,且在R=0.1764nm与A2Δ态发生交叉,导致SiH最主要的电子激发跃迁A2Δ-X2Π中仅主要观测到(0-0)带,这与实验结果完全一致.C2∑+和D2∑+态在R=0.1799nm处发生由于对称性相同而出现回避交叉.对于束缚态X2Π,A2Δ,D2∑+和a4∑-,数值求解核运动的径向Schrdinger方程预测出各电子态所有可能的振动能级和转动常数,进而拟合得到的光谱常数与已有的实验数据符合较好.     

Multi-reference configuration-interaction calculations on multiply charged ions of carbon monosulfide

The potential energy curves for neutrals and multiply charged ions of carbon monosulfide are computed with highly correlated multi-reference configuration interaction wavefunctions.The correlations of inner-shell electrons with the scalar relativistic effects are included in the present computations.The spectroscopic constants,dissociation energies,ionization energies for ground and low-lying excited states together with corresponding electronic configurations of ions are obtained,and a good agreement between the present work and existing experiments is found.No theoretical evidence is found for the adiabatically stable CSq+(q>2) ions according to the present ab initio calculations.The calculated values for 1st-6th ionization energies are 11.25,32.66,64.82,106.25,159.75,and 224.64 eV,respectively.The kinetic energy release data of fragments are provided by the present work for further experimental comparisons.     

Ab initio calculation of the ground and first excited states of the lithium dimer

Based on a high level ab initio calculation which is carried out with the multireference configuration interaction method under the aug-cc-pVXZ (AVXZ) basis sets, X=T, Q, 5, the accurate potential energy curves (PECs) of the ground state ${\rm{X}}{}^{{\rm{1}}}{\rm{\Sigma }}_{g}^{+}$ and the first excited state ${\rm{A}}{}^{{\rm{1}}}{\rm{\Sigma }}_{u}^{+}$ of Li₂ are constructed. By fitting the ab initio potential energy points with the Murrell–Sorbie potential function, the analytic potential energy functions (APEFs) are obtained. The molecular bond length at the equilibrium (R_e), the potential well depth (D_e), and the spectroscopic constants (B_e, ω_e, α_e, and ω_eχ_e) for the ${\rm{X}}{}^{{\rm{1}}}{\rm{\Sigma }}_{g}^{+}$ state and the ${\rm{A}}{}^{{\rm{1}}}{\rm{\Sigma }}_{u}^{+}$ state are deduced from the APEFs. The vibrational energy levels of the two electronic states are obtained by solving the time-independent Schrödinger equation with the Fourier grid Hamiltonian method. All the spectroscopic constants and the vibrational levels agree well with the experimental results. The Franck–Condon factors (FCFs) corresponding to the transitions from the vibrational level (v′=0) of the ground state to the vibrational levels (v″=0–74) of the first excited state have been calculated. The FCF for the vibronic transition of ${\rm{A}}{}^{{\rm{1}}}{\rm{\Sigma }}_{u}^{+}$(v″=0) ←${\rm{X}}{}^{{\rm{1}}}{\rm{\Sigma }}_{g}^{+}$(v′=0) is the strongest. These PECs and corresponding spectroscopic constants provide reliable theoretical references to both the spectroscopic and the molecular dynamic studies of the Li₂ dimer.     

LiAl分子基态、激发态势能曲线和振动能级

利用单双激发多参考组态相互作用方法获得了LiAl分子基态X¹∑⁺及七个激发态a³∏, A¹∏, b³∑⁺, c³∑⁺, B¹∏, C¹∑⁺, d³∏的势能曲线, 通过势能曲线得到各态的平衡核间距R_e, 进而求得绝热激发能和垂直激发能.计算结果表明:c³∑⁺ 电子态是一个不稳定的排斥态, A¹∏态是一个较弱的束缚态, 其余6个电子态均为束缚态; b³∑⁺与 c³∑⁺态之间存在预解离现象; 8个电子态分别解离到两个通道, 即Li(²S)+Al(²P⁰)与Li(²P⁰)+Al(²P⁰). 接着将势能曲线拟合到Murrel-Sorbie解析势能函数形式, 据此获得各态的光谱数据:基态X¹∑⁺的平衡键长为0.2863 nm, 谐振频率为316 cm^-1, 解离能D_e为1.03 eV, 激发态a³∏, A¹∏, b³∑⁺, c³∑⁺, B¹∏, C¹∑⁺, d³∏的垂直激发能依次为0.27, 0.83, 1.18, 1.14, 1.62, 1.81, 2.00 eV; 解离能依次为1.03, 0.82, 0.26, 排斥态, 1.54, 1.10, 0.93 eV, 相应谐振频率 ω_e为339, 237, 394, 排斥态, 429, 192, 178 cm^-1. 通过求解核运动的薛定谔方程找到了J=0时 LiAl分子7个束缚电子态的振动能级和转动惯量. 关键词： LiAl 光谱常数 势能曲线 振动能级     

Ab initio investigation of sulfur monofluoride and its singly charged cation and anion in their ground electronic state

The SF radical and its singly charged cation and anion, SF+and SF-, have been investigated on the MRCI/aug-ccp VX Z(X = Q, 5, 6) levels of theory with Davidson correction. Both the core–valence correlation and the relativistic effect are considered. The extrapolating to the complete basis set(CBS) limit is adopted to remove the basis set truncation error.Geometrical parameters, potential energy curves(PECs), vibrational energy levels, spectroscopic constants, ionization potentials, and electron affinities of the ground electronic state for all these species are obtained. The information with respect to molecular characteristics of the SFn(n =-1, 0, +1) systems derived in this work will help to extend our knowledge and to guide further experimental or theoretical researches.     

VPT2+K spectroscopic constants and matrix elements of the transformed vibrational Hamiltonian of a polyatomic molecule with resonances using Van Vleck perturbation theory

Vibrational levels of polyatomic molecules are analysed with Van Vleck perturbation theory to connect experimental energy levels to computed molecular potential energy surfaces. Vibrational matrix elements are calculated from a quartic potential function via second-order Van Vleck perturbation theory, a procedure that treats both weak and strong interactions among vibrational states by approximately block-diagonalising the vibrational Hamiltonian. A clear and complete derivation of anharmonic and resonance constants as well as general expressions for both on- and off-diagonal matrix elements of the transformed Hamiltonian is presented. The equations are written in partial fraction form and as a constant multiplied by a harmonic oscillator matrix element to facilitate removing the effect of strongly interacting resonant states both in analytical formulae and in computer code. The derived equations are validated numerically, and results for the isotopomers of formaldehyde (H₂CO, HDCO, D₂CO) are included. The implications of the equations on zero-point energy calculations and experimental fits are discussed. The VPT2+K method is defined by these results for use in fitting and calculating vibrational energy levels.     

双原子分子振动能谱与离解能的精确研究

代数方法(AM)的建立解决了实验方法和精确量子力学理论方法难以获得双原子分子的包含最高振动能级在内的所有高阶振动能级的精确数值这一问题.基于LeRoy与Bernstein的工作,孙卫国等又建立了精确计算双原子分子离解能的新解析表达式.应用新公式和代数方法(AM),研究了一些双原子分子部分电子态的振动能谱和分子离解能,获得了与实验值符合非常好的理论结果.该方法在理论上提供了获得双原子分子完全振动能谱和精确分子离解能的物理新方法.     

A local framework for calculating coupled cluster singles and doubles excitation energies (LoFEx-CCSD)

ABSTRACT

The recently developed Local Framework for calculating Excitation energies (LoFEx) is extended to the coupled cluster singles and doubles (CCSD) model. In the new scheme, a standard CCSD excitation energy calculation is carried out within a reduced excitation orbital space (XOS), which is composed of localised molecular orbitals and natural transition orbitals determined from time-dependent Hartree–Fock theory. The presented algorithm uses a series of reduced second-order approximate coupled cluster singles and doubles (CC2) calculations to optimise the XOS in a black-box manner. This ensures that the requested CCSD excitation energies have been determined to a predefined accuracy compared to a conventional CCSD calculation. We present numerical LoFEx-CCSD results for a set of medium-sized organic molecules, which illustrate the black-box nature of the approach and the computational savings obtained for transitions that are local compared to the size of the molecule. In fact, for such local transitions, the LoFEx-CCSD scheme can be applied to molecular systems where a conventional CCSD implementation is intractable.     

Studies on dissociation energies of diatomic molecules using vibrational spectroscopic constants

New analytical expression and numerical approach are suggested to calculate dissociation energies De of diatomic molecular states using an extreme value method (EVM). Studies on some electronic states of OH, BH, N2, Br2, ClF and CO molecules show that the accuracy of the EVM dissociation energies depends on the number of correct vibrational constants used in the calculations. The convergence qualities of De are suggested to be an alternative physical criterion to measure the qualities of the various sets of vibrational constants from different literature for the same diatomic state.     

Ab initio study of PN electronic states – a qualitative interpretation of the perturbation and predissociation effects on observed transitions

Valence and high electronic states of PN have been calculated with accurate quantum chemistry methods. The variety of theoretical methods used includes complete active space self-consistent field, multireference configuration interaction and the newly developed explicitly correlated coupled cluster methods. The large correlation-consistent atomic orbitals basis sets AVQZ, AV5Z and AV(5+d)Z are used for the potential energy curves calculations in the bonding and long-range regions. The spectroscopic constants (R_e, B_e, ω_e, ω_ex_e, α_e, D_e, T_e) and the vibrational levels of the bound valence states (X¹Σ⁺, A¹Π, a³Σ⁺, d ³Δ, e³Σ^?, C¹Σ^?, b³Π, D ¹Δ and E¹Σ⁺ and some higher bound states) are determined and compared with experimental findings when available. Significant spin–orbit interactions between triplet states and A¹Π and E¹Σ⁺ excited states are found near the crossing points of the potential energy curves and could explain predissociation phenomena and the perturbations of the vibrational levels experimentally observed for PN in their A¹Π and E¹Σ⁺ states.     

Theoretical study of the SrLi+ molecular ion: structural,electronic and dipolar properties

ABSTRACT

The structural and electronic properties of (SrLi)⁺ molecular ion have been determined by the use of ab initio approaches. Potential energy curves (PECs) with their spectroscopic constants (R_e, D_e, ω_e, T_e, B_e and ω_eχ_e) have been calculated. Also, the vibrational properties and the electric dipole moments, either permanent (PDM) or transition (TDM) ones, have been investigated and analysed. Large Gaussian basis sets, the full valence configuration interaction (FCI) and the formalism of non-empirical pseudo-potential including the two approaches, effective core potential (ECP) and core polarisation potential (CPP), are analysed. Therefore, (SrLi)⁺ is considered as a two effective electrons system. Numerous excited states of symmetries ^1,3Σ⁺, ^1,3Π and ^1,3Δ dissociating below the ionic limit Sr²⁺Li^? have been investigated. This study shows interesting behaviours around the avoided crossing related to charge transfer involving important processes in physics and astrophysics such as dynamics, pre-dissociation and inelastic transitions.     

LiC分子基态及其低电子激发态的多参考组态相互作用方法研究

采用包含Davidson修正的多参考组态相互作用(MRCI+Q)方法结合6-311++G(3df,3pd)基组计算了LiC分子基态(X4Σ-)以及五个低电子激发态(a2Π,b2Δ,c2Σ-,d2Σ+,A4Π)的势能曲线.将得到的势能曲线拟合到Murrell-Sorbie解析势能函数形式,确定了对应态的平衡结构Re、谐振频率ωe和离解能De等光谱数据,计算值与仅有的几个其他结果进行了比较.通过求解核运动的薛定谔方程首次报道了LiC分子几个低电子态在J=0下的振动能级、转动惯量和六个离心畸变常数(Dν,Hν,Lν,Mν,Nν和Oν).     

Accurate vibrational energy spectra and dissociation energies of some diatomic electronic states

An algebraic method (AM) used to study the full vibrational spectra of diatomic systems, and an analytical formula used to calculate accurate molecular dissociation energies are applied to study the full vibrational spectra and molecular dissociation energies of some electronic states of homonuclear and heteronuclear diatomic molecules and diatomic ions. Studies show that the AM method and the analytical expression are reliable and economical physical methods for studying full vibrational spectra and molecular dissociation energies of diatomic electronic systems theoretically. They are particularly useful for those diatomic systems whose high-lying vibrational energies may not be available.      

Excited state geometry optimisation using Fock-space multi-reference coupled cluster method

The Fock-space multi-reference coupled cluster method is used for the geometry optimisation of the low-lying excited states of the molecules. Molecular geometries of the carbon monohydride cation (CH)⁺, water (H₂O), ozone (O₃) and formaldehyde (HCHO) in their low-lying excited states are optimised. Excited state gradients are calculated using finite field multi-reference coupled cluster method. We compare our results with other theoretical and/or experimental results, wherever available.     

多参考组态相互作用方法研究ZnHg低激发态(1∏，3∏)的势能曲线和解析势能函数

采用多参考组态相互作用方法计算了ZnHg二聚体两个低激发∏态(¹∏，³∏)的原子间相互作用势能曲线. 用Murrel-Sorbie函数拟合得到了相应的解析势能函数，并用其计算力常数，进而确定了光谱常数. 所得结果与仅有的理论工作进行了比较. 基于所得势能曲线，通过解分子中原子核运动的薛定谔方程预测了各电子态的振动能级. 关键词： 势能曲线 解析势能函数 光谱常数 振动能级